Refined Iterated Pareto Greedy for Energy-aware Hybrid Flowshop Scheduling with Blocking Constraints

TL;DR

This work tackles energy-efficient scheduling for blocking hybrid flowshops (BHFS) by formulating a novel bi-objective MILP that minimizes $C_{max}$ and total energy consumption $TEC$, while explicitly modeling idle and blocking times and machine turn-on/off dynamics. It contributes an augmented $ ext{epsilon}$-constraint method to generate Pareto fronts and introduces Refined Iterated Pareto Greedy (R-IPG), a scalable metaheuristic with initialization, selection, greedy reconstruction, local search, and refining phases to approximate the Pareto frontier for large instances. Computational experiments across small, medium, and large BHFS benchmarks demonstrate that RIPG achieves superior convergence and solution diversity, outperforming NSGA-II and MOIG on larger problems, with the exact augmented epsilon-constraint MILP providing strong baselines. The findings have practical implications for energy-aware production planning, offering robust tools to balance throughput and energy use in complex manufacturing settings while highlighting avenues for stochastic, dynamic, and distributed extensions.

Abstract

The scarcity of non-renewable energy sources, geopolitical problems in its supply, increasing prices, and the impact of climate change, force the global economy to develop more energy-efficient solutions for their operations. The Manufacturing sector is not excluded from this challenge as one of the largest consumers of energy. Energy-efficient scheduling is a method that attracts manufacturing companies to reduce their consumption as it can be quickly deployed and can show impact immediately. In this study, the hybrid flow shop scheduling problem with blocking constraint (BHFS) is investigated in which we seek to minimize the latest completion time (i.e. makespan) and overall energy consumption, a typical manufacturing setting across many industries from automotive to pharmaceutical. Energy consumption and the latest completion time of customer orders are usually conflicting objectives. Therefore, we first formulate the problem as a novel multi-objective mixed integer programming (MIP) model and propose an augmented epsilon-constraint method for finding the Pareto-optimal solutions. Also, an effective multi-objective metaheuristic algorithm. Refined Iterated Pareto Greedy (RIPG), is developed to solve large instances in reasonable time. Our proposed methods are benchmarked using small, medium, and large-size instances to evaluate their efficiency. Two well-known algorithms are adopted for comparing our novel approaches. The computational results show the effectiveness of our method.

Figures (8)

• Figure 1: Gantt chart with minimum makespan (Cmax)
• Figure 2: Gantt chart with minimum Total Energy Consumption (TEC)
• Figure 3: Flowchart of the proposed R-IPG
• Figure 4: $I_h$ means plots for the R-IPG parameters
• Figure 5: $GD$ means plots for the R-IPG parameters